Theoretical analysis for moiré deflectometry from diffraction theory

Theories of moire deflectometry are presented based on scalar diffraction theory. It is shown that the moire effect is not a pure geometric phenomenon but actually the result of multishearing interference. By performing zeroth-order or first-order filtering, the field in the plane of observation is seen to be the result of double- or triple-shearing interference, respectively. With first-order filtering, the intensity distribution is proved to be a strict cosinusoidal intensity distribution, and the diffraction effect, which depends on the distance between two gratings, affects just the phase shift of the moire fringes. Compared with previous research, a more precise relation between the unwrapped phase and the deflection angles is obtained. The results will be very useful for image processing of moire patterns with Fourier transform profilometry and phase-shift methods.